# How can nucleophilicity be estimated accurately?

Given the following: $\ce{CN-,OH-,SH-,I-}$. Determine the relative order of nucleophilicity in a protic solvent.

I know that, more the nucleophile is solvated by hydrogen bonding in a protic solvent, the lesser will be its nucleophilicity. Also, solvation depends upon the size of the anionic nucleophile or its charge density (smaller the size greater the solvation).

Again larger the size, greater will be the polarizability of the anionic nucleophile and thus stronger will be its nucleophilicity.

All these indicate that the larger the size, the greater the nucleophilicity will be, and so the relative order of nucleophilicity should be $\ce{I-}>\ce{SH-}>\ce{CN-}>\ce{OH-}$. But the answer is $\ce{SH-}>\ce{CN-}>\ce{I-}>\ce{OH-}$. So where have I gone wrong? How can I determine nucleophilicity accurately? Is there any other factor on which nucleophilicity depends?

$$\lg k_\pu{20^\circ C} = s_\mathrm{N}(N + E)\tag{1}$$
where $E$ is an electrophilicity parameter, $N$ is a nucleophilicity parameter and $s_\mathrm{N}$ is a solvent and nucleophile-dependent additional nucleophilicity factor. A multitude of nucleophiles and electrophiles have been entered into this scheme over the years and a few posters showing nucleophilicity scales have been created (see the webpage).